Warm start generalized additive mixed-effect (game) framework

ABSTRACT

In an example embodiment, a warm-start training solution is used to dramatically reduce the computational resources needed to train when retraining a generalized additive mixed-effect (GAME) model. The problem of retraining time is particularly applicable to GAME models, since these models take much longer to train as the data grows. In the past, the strategy to reduce computational resources during retraining was to use less training data, but this affects the model quality, especially for GAME models, which rely on fine-grained sub-models at, for example, member or item levels. The present solution addresses the computational resources issues without sacrificing GAME model accuracy.

TECHNICAL FIELD

The present disclosure generally relates to technical problems encountered in providing machine learning on computer systems. More specifically, the present disclosure relates to a warm start GAME framework.

BACKGROUND

The rise of the Internet has occasioned two disparate yet related phenomena: the increase in the presence of social networking services, with their corresponding member profiles visible to large numbers of people, and the increase in the use of these social networking services to perform searches or obtain information. An example of a common search or recommendation provided on a social networking service is the search for jobs that have been posted on, or linked to by, the social networks.

A technical problem encountered by social networking services in managing online job searches is that determining how to serve the most appropriate and relevant information with minimal delay becomes significantly challenging as the number of sources and volumes of information shared via the social networking services grows at an unprecedented pace. This includes determining how to recommend, for example, job openings and course offerings as well as determining which feed items to surface in an online feed.

Personalization of job search and other results is also desirable. For example, when users search for a query like “software engineer,” depending on the skills, background, experience, location, and other factors about the users, the odds that the users will interact with the results (such as by applying to an underlying job) can be drastically different. For example, a person skilled in user interfaces would see a very different set of job results compared to someone specializing in hardware. Indeed, even people having the same skill sets and current job could have different odds of interacting with the same results.

Results may also be presented without an explicit search performed by a user, specifically in the form of recommendations. Recommender systems are automated computer programs that match items to users in different contexts. In order to achieve accurate recommendations on a large scale, machine learned models are used to estimate user preferences from user feedback data. Such models are constructed using large amounts of high-frequency data obtained from past user interactions with objects or results.

Historically, models to rank job search results in response to a query or perform other recommendations have heavily utilized text and entity-based features extracted from the query and job postings to derive a global ranking or recommendation. An example of such models is a generalized linear model (GLM). A GLM is a generalization of linear regression that allows for response variables that have error distribution models other than a normal distribution. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. GLMs may utilize the following prediction formula: g(E[y_(ij)])=x′_(ij)w, where this formula predicts the response of user i to item j, and x_(ij) is a feature vector, w is a coefficient vector, E[y_(ij)] is an expectation of response, and g( ) is a link function.

However, in scenarios where data is abundant, having a more fine-grained model at the user or item level would potentially lead to more accurate prediction, because the user's personal preferences on items and the item's specific attraction for users could be better captured.

Use of a generalized additive mixed-effect (GAME) framework provides significant power and scalability in modeling personalized interactions. While the GAME framework is very powerful and scalable in modeling personalized interactions, its performance is subject to the input knowledge of different types of entities (e.g., member jobs, news updates, etc.) (in other words, “random” effects). The deeper the understanding of these entities and the interactions among them, the better the modeling outcomes. This typically relies on GAME models using more data during training, and training on more random effects, to achieve satisfactory modeling performance. However, from the technical perspective, adding more training data and more random effects increases model training times and uses more computational resources.

BRIEF DESCRIPTION OF THE DRAWINGS

Some embodiments of the technology are illustrated, by way of example and not limitation, in the figures of the accompanying drawings.

FIG. 1 is a block diagram illustrating a client-server system in accordance with an example embodiment.

FIG. 2 is a block diagram showing the functional components of a social networking service, including a data processing module referred to herein as a search engine, for use in generating and providing search results for a search query, consistent with some embodiments of the present disclosure.

FIG. 3 is a block diagram illustrating an application server module of FIG. 2 in more detail, in accordance with an example embodiment.

FIG. 4 is a block diagram illustrating the job posting result ranking engine 310 of FIG. 3 in more detail, in accordance with an example embodiment.

FIG. 5 is a flow diagram illustrating a method for training a generalized additive mixed effect model, in accordance with an example embodiment.

FIG. 6 is a screenshot of a user teed that includes items in different categories, according to some example embodiments.

FIG. 7 is a block diagram illustrating a software architecture, in accordance with an example embodiment.

FIG. 8 illustrates a diagrammatic representation of a machine in the form of a computer system within which a set of instructions may be executed for causing the machine to perform any one or more of the methodologies discussed herein, according to an example embodiment.

DETAILED DESCRIPTION Overview

The present disclosure describes, among other things, methods, systems, and computer program products that individually provide various functionality. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the various aspects of different embodiments of the present disclosure. It will be evident, however, to one skilled in the art, that the present disclosure may be practiced without all of the specific details.

In an example embodiment, a warm-start training solution is used to dramatically reduce the computational resources needed to train when retraining a GAME model. The problem of retraining time is particularly applicable to GAME models, since these models take much longer to train as the data grows. In the past, the strategy to reduce computational resources during retraining was to use less training data, but this affects the model quality, especially for GAME models, which rely on fine-grained sub-models at, for example, member or item levels. The present solution addresses the computational resources issues without sacrificing GAME model accuracy.

One approach for better capturing a user's personal preference for items and an item's specific attraction for users in prediction/recommender systems would be to introduce ID-level regression coefficients in addition to the global regression coefficients in a GLM setting. Such a solution is known as a generalized linear mixed model (GLMix). However, for large data sets with a large number of ID-level coefficients, fitting a GLMix model can be computationally challenging, especially as the solution scales.

A GAME model is essentially a single model made up of other models, specifically a fixed effects model and at least one random effects model. The outputs of these individual models are combined for the final GAME model output. Each of these models has different granularities and dimensions. A global model may model the similarity between user attributes (e.g., from the member profile or activity history) and item attributes. A per-user model may model user attributes and activity history. A per-item model may model item attributes and activity history.

In the context of a job search result ranking or recommendation, this results in the following components:

-   -   a global model that captures the general behavior of how members         apply for jobs     -   a member-specific model with parameters (to be learned from         data) specific to the given member to capture the member's         personal behavior that deviates from the general behavior, and     -   a job-specific model with parameters (to be learned from data)         specific to the given job to capture the job's unique behavior         that deviates from the general behavior.

Each of the models within the larger GAME model (which may be referred to herein as portions of the GAME model) may also contain offsets. These offsets are values added to a score calculated by a model prior to it going through a link function or link layer. In GAME, the offset is the score from the previous coordinate in the same model. It is used as a way for more personalized models to overrule a default model.

FIG. 1 is a block diagram illustrating a client-server system 100, in accordance with an example embodiment. A networked system 102 provides server-side functionality via a network 104 (e.g., the Internet or a wide area network (WAN)) to one or more clients. FIG. 1 illustrates, for example, a web client 106 (e.g., a browser) and a programmatic client 108 executing on respective client machines 110 and 112.

An application program interface (API) server 114 and a web server 116 are coupled to, and provide programmatic and web interfaces respectively to, one or more application servers 118. The application server(s) 118 host one or more applications 120. The application server(s) 118 are, in turn, shown to be coupled to one or more database servers 124 that facilitate access to one or more databases 126. While the application(s) 120 are shown in FIG. 1 to form part of the networked system 102, it will be appreciated that, in alternative embodiments, the application(s) 120 may form part of a service that is separate and distinct from the networked system 102.

Further, while the client-server system 100 shown in FIG. 1 employs a client-server architecture, the present disclosure is, of course, not limited to such an architecture, and could equally well find application in a distributed, or peer-to-peer, architecture system, for example. The various applications 120 could also be implemented as standalone software programs, which do not necessarily have networking capabilities.

The web client 106 accesses the various applications 120 via the web interface supported by the web server 116. Similarly, the programmatic client 108 accesses the various services and functions provided by the application(s) 120 via the programmatic interface provided by the API server 114.

FIG. 1 also illustrates a third-party application 128, executing on a third-party server 130, as having programmatic access to the networked system 102 via the programmatic interface provided by the API server 114. For example, the third-party application 128 may, utilizing information retrieved from the networked system 102, support one or more features or functions on a website hosted by a third party. The third-party website may, for example, provide one or more functions that are supported by the relevant applications 120 of the networked system 102.

In some embodiments, any website referred to herein may comprise online content that may be rendered on a variety of devices including, but not limited to, a desktop personal computer (PC), a laptop, and a mobile device (e.g., a tablet computer, smartphone, etc.). In this respect, any of these devices may be employed by a user to use the features of the present disclosure. In some embodiments, a user can use a mobile app on a mobile device (any of the machines 110, 112 and the third-party server 130 may be a mobile device) to access and browse online content, such as any of the online content disclosed herein. A mobile server (e.g., API server 114) may communicate with the mobile app and the application server(s) 118 in order to make the features of the present disclosure available on the mobile device.

In some embodiments, the networked system 102 may comprise functional components of a social networking service. FIG. 2 is a block diagram showing the functional components of a social networking system 210, including a data processing module referred to herein as a search engine 216, for use in generating and providing search results for a search query, consistent with some embodiments of the present disclosure. In some embodiments, the search engine 216 may reside on the application server(s) 118 in FIG. 1. However, it is contemplated that other configurations are also within the scope of the present disclosure.

As shown in FIG. 2, a front end may comprise a user interface module (e.g., a web server 116) 212, which receives requests from various client computing devices, and communicates appropriate responses to the requesting client devices. For example, the user interface module(s) 212 may receive requests in the form of Hypertext Transfer Protocol (HTTP) requests or other web-based API requests. In addition, a user interaction detection module 213 may be provided to detect various interactions that members have with different applications 120, services, and content presented. As shown in FIG. 2, upon detecting a particular interaction, the user interaction detection module 213 logs the interaction, including the type of interaction and any metadata relating to the interaction, in a member activity and behavior database 222.

An application logic layer may include one or more various application server modules 214, which, in conjunction with the user interface module(s) 212, generate various user interfaces (e.g., web pages) with data retrieved from various data sources in a data layer. In some embodiments, individual application server modules 214 are used to implement the functionality associated with various applications 120 and/or services provided by the social networking service.

As shown in FIG. 2, the data layer may include several databases 126, such as a profile database 218 for storing profile data, including both user profile data and profile data for various organizations (e.g., companies, schools, etc.). Consistent with some embodiments, when a person initially registers to become a user of the social networking service, the person will be prompted to provide some personal information, such as his or her name, age (e.g., birthdate), gender, interests, contact information, home town, address, spouse's and/or family members' names, educational background (e.g., schools, majors, matriculation and/or graduation dates, etc.), employment history, skills, professional organizations, and so on. This information is stored, for example, in the profile database 218. Similarly, when a representative of an organization initially registers the organization with the social networking service, the representative may be prompted to provide certain information about the organization. This information may be stored, for example, in the profile database 218, or another database (not shown). In some embodiments, the profile data may be processed (e.g., in the background or offline) to generate various derived profile data. For example, if a member has provided information about various job titles that the member has held with the same organization or different organizations, and for how long, this information can be used to infer or derive a member profile attribute indicating the member's overall seniority level, or seniority level within a particular organization. In some embodiments, importing or otherwise accessing data from one or more externally hosted data sources may enrich profile data for both members and organizations. For instance, with organizations in particular, financial data may be imported from one or more external data sources and made part of an organization's profile. This importation of organization data and enrichment of the data will be described in more detail later in this document.

Once registered, a user may invite other members, or be invited by other members, to connect via the social networking service. A “connection” may constitute a bilateral agreement by the users, such that both users acknowledge the establishment of the connection. Similarly, in some embodiments, a user may elect to “follow” another user. In contrast to establishing a connection, the concept of “following” another user typically is a unilateral operation and, at least in some embodiments, does not require acknowledgement or approval by the user that is being followed. When one user follows another, the user who is following may receive status updates (e.g., in an activity or content stream) or other messages published by the user being followed, relating to various activities undertaken by the user being followed. Similarly, when a user follows an organization, the user becomes eligible to receive messages or status updates published on behalf of the organization. For instance, messages or status updates published on behalf of an organization that a user is following will appear in the user's personalized data feed, commonly referred to as an activity stream or content stream. In any case, the various associations and relationships that the users establish with other users, or with other entities and objects, are stored and maintained within a social graph in a social graph database 220.

As users interact with the various applications 120, services, and content made available via the social networking service, the users' interactions and behavior (e.g., content viewed, links or buttons selected, messages responded to, etc.) may be tracked, and information concerning the users' activities and behavior may be logged or stored, for example, as indicated in FIG. 2, by the user activity and behavior database 222. This logged activity information may then be used by the search engine 216 to determine search results for a search query.

In some embodiments, the databases 218, 220, and 222 may be incorporated into the database(s) 126 in FIG. 1. However, other configurations are also within the scope of the present disclosure.

Although not shown, in some embodiments, the social networking system 210 provides an API module via which applications 120 and services can access various data and services provided or maintained by the social networking service. For example, using an API, an application may be able to request and/or receive one or more recommendations. Such applications 120 may be browser-based applications 120, or may be operating system-specific. In particular, some applications 120 may reside and execute (at least partially) on one or more mobile devices (e.g., phone or tablet computing devices) with a mobile operating system. Furthermore, while in many cases the applications 120 or services that leverage the API may be applications 120 and services that are developed and maintained by the entity operating the social networking service, nothing other than data privacy concerns prevents the API from being provided to the public or to certain third parties under special arrangements, thereby making the navigation recommendations available to third-party applications 128 and services.

Although the search engine 216 is referred to herein as being used in the context of a social networking service, it is contemplated that it may also be employed in the context of any website or online services. Additionally, although features of the present disclosure are referred to herein as being used or presented in the context of a web page, it is contemplated that any user interface view (e.g., a user interface on a mobile device or on desktop software) is within the scope of the present disclosure.

In an example embodiment, when user profiles are indexed, forward search indexes are created and stored. The search engine 216 facilitates the indexing and searching for content within the social networking service, such as the indexing and searching for data or information contained in the data layer, such as profile data (stored, e.g., in the profile database 218), social graph data (stored, e.g., in the social graph database 220), and member activity and behavior data (stored, e.g., in the member activity and behavior database 222), as well as job postings. The search engine 216 may collect, parse, and/or store data in an index or other similar structure to facilitate the identification and retrieval of information in response to received queries for information. This may include, but is not limited to, forward search indexes, inverted indexes, N-gram indexes, and so on.

For purposes of this document, the warm start solution for GAME modeling is described with respect to models pertaining to job recommendations in a social networking service. Nevertheless, one of ordinary skill in the art will recognize that these techniques can be applied to other types of models in social networking services, such as feed recommendations, profile recommendations, course suggestions, etc.

FIG. 3 is a block diagram illustrating application server module 214 of FIG. 2 in more detail, in accordance with an example embodiment. While in many embodiments, the application server module 214 will contain many subcomponents used to perform various different actions within the social networking system, in FIG. 3 only those components that are relevant to the present disclosure are depicted. A job posting query processor 300 comprises a query ingestion component 302, which receives a user input “query” related to a job posting search via a user interface (not pictured). Notably, this user input may take many forms. In some example embodiments, the user may explicitly describe a job posting search query, such as by entering one or more keywords or terms into one or more fields of a user interface screen. In other example embodiments, the job posting query may be inferred based on one or more user actions, such as selection of one or more filters, other job posting searches by the user, searches for other users or entities, and the like.

This “query” may be sent to a job posting database query formulation component 304, which formulates an actual job posting database query, which will be sent, via a job posting database interface 306, to job posting database 308. Job posting results responsive to this job posting database query may then be sent to the job posting result ranking engine 310, again via the job posting database interface 306. The job posting result ranking engine 310 then ranks the job posting results and sends the ranked job posting results back to the user interface for display to the user.

FIG. 4 is a block diagram illustrating job posting result ranking engine 310 of FIG. 3 in more detail, in accordance with an example embodiment. The job posting result ranking engine 310 may use machine learning techniques to learn a job posting result ranking model 400, which can then be used to rank actual job posting results from the job posting database 308.

The job posting result ranking engine 310 may comprise a training component 402 and a job posting result processing component 404. The training component 402 feeds sample job postings results 406 and sample member data 407 into a feature extractor 408 that extracts one or more features 410 for the sample job postings results 406 and sample member data 407. The sample job postings results 406 may each include job postings results produced in response to a particular query as well as one or more labels, such as a job posting application likelihood score, which is a score indicating a probability that a user with corresponding sample member data 407 will apply for the job associated with the corresponding sample job postings result 406.

Sample member data 407 may include, for example, a history of job searches and resulting expressions of interest (such as clicking on job posting results or applications to corresponding jobs) in particular job posting results for particular users. In some example embodiments, sample member data 407 can also include other data relevant for personalization of the query results to the particular user, such as a user profile for the member or a history of other user activity.

A machine learning algorithm 412 produces the job posting result ranking model 400 using the extracted features 410 along with the one or more labels. In the job posting result processing component 404, candidate job postings results 414 resulting from a particular query are fed to a feature extractor 416 along with member data 415. The feature extractor 416 extracts one or more features 418 from the candidate job postings results 414 and member data 415. These features 418 are then fed to the job posting result ranking model 400, which outputs a job posting application likelihood score for each candidate job postings result for the particular query.

This job posting application likelihood score for each candidate job posting result may then be passed to a job posting result sorter 420, which may sort the candidate job postings results 414 based on their respective job posting application likelihood scores.

It should be noted that the job posting result ranking model 400 may be periodically updated via additional training and/or user feedback. The user feedback may be either feedback from members performing searches or from companies corresponding to the job postings. The feedback may include an indication about how successful the job posting result ranking model 400 is in predicting member interest in the job posting results presented.

The machine learning algorithm 412 may be selected from among many different potential supervised or unsupervised machine learning algorithms 412. Examples of supervised learning algorithms include artificial neural networks, Bayesian networks, instance-based learning, support vector machines, random forests, linear classifiers, quadratic classifiers, k-nearest neighbor, decision trees, and hidden Markov models. Examples of unsupervised learning algorithms include expectation-maximization algorithms, vector quantization, and information bottleneck method. In an example embodiment, a multi-class logistical regression model is used.

Of course, the above techniques can be extended to other types of models than ranking models, such as job posting result ranking model 400. For example, rather than use the predictions to rank job results in response to a query, a system could use the predictions to recommend one or more job postings to a user without the user expressly requesting a job search. Furthermore, the techniques can be extended to other types of predictions for items other than job postings or job results, such as feed objects.

Rather than passing the extracted features 410 directly to the machine learning algorithm 412, in an example embodiment they are first passed through a retraining component 413. The retraining component 413 executes an automated procedure for determining whether retraining will occur, when it will occur, and how it will occur.

Specifically, the retraining component 413 combines a full training strategy with a subset training strategy. Training data may be divided based on time into intervals. When first training the model, the first interval's training data may be used to train the initial GAME model. For subsequent intervals, however, the previously trained model(s) are loaded and rolled into the training procedure.

The following pseudo-code describes the algorithm that can be used by the retraining component 413 in an example embodiment.

 1. Partition data based on Time into K intervals  2. For the first interval:  3.  Train a GAME model: Fixed Effect + M Random Effects  4.  Index the GAME model to Time 0  5. For each subsequent interval Time i:  6.  Load previous GAME model Time i-1: Fixed Effect +  M Random Effects  7.  For j −> 0: N outer loops until convergence:  8.   Retrain Fixed Effect using Time i data:  9.    Use Fixed Effect coefficients from Time i-1 but converge  on data from Time i 10.    Update Fixed Effect Offsets for each data point 11.   For each Random Effect (RE): 12.   Train each RE instance in parallel on Time i data: 13.    If Number of data points < Threshold: 14.     No training for this instance: use Time i-1 model 15.    Else: 16.     Retrain on Time i data (Minimize Σ     L(x, β) + λ * ∥ β − b ∥²) 17.   Update Random Effect Offsets for each data point

Specifically, a base GAME model is trained using the data from the first time interface T₁. This model becomes the initial model M₁. Subsequently, the training process is warm started by training using model M_(i−1) as a base, with i being the current time interval. Thus, for example, assume a simple training data example where a first time interval includes training data from member 1 and member 3, a second time interval includes training data from member 2, and a third time interval includes training data from member 3. First, the data from the first time interval (member 1 and member 3) is used to train the base model. This GAME base model will be composed of a fixed effect model and two random effect models (one for member 1 and one for member 3).

For each subsequent interval, the previous GAME model is loaded. The fixed effect portion of the previous GAME model is retrained using the new data for this interval (for example, in the second time interval this would be the training data from member 2). However, during this retraining the fixed effect coefficients from the previous time interval are used while converging on data from the current time interval. Convergence occurs when a subsequent version of the GAME model differs from an immediately preceding version of the GAME model by less than a second threshold. Following this convergence, the fixed effect offsets can be updated for each data point in the training data from this time interval.

Each random effect in the training data may then be considered for use in possibly training or retraining a corresponding random effect portion of the GAME model. Specifically, a threshold may be used to determine if the retraining should occur at all. Specifically, if there are too few data points in a particular time interval to significantly alter the random effect portion of the GAME model, then the retraining component 413 will not retrain but simply use the corresponding random effect portion from the previous version of the GAME model. It should be noted that the use of this threshold is optional in that it is possible to set the threshold to zero data points, which would result in the retraining component 413 always determining to retrain, at least for the threshold determination.

In an optional extension to this, even once the retraining component 413 decides to retrain the corresponding random effects portion of the GAME model, this retraining is done in a way to bias the new model towards the old one. The benefit of this is that an existing model, which presumably is of sufficient quality to have been accepted in the first place, can then also be presumed to be an accurate representation of the behavior/preferences of a user or entity. By biasing the new model towards the old one, the new model is resilient towards anomalous data. Here, then the training can occur by minimizing ΣL(x, β)+λ*∥β−b∥², where b is the coefficient of the existing model.

Specifically, x is a feature vector associated with one or more features extracted from the training data in the interval associated with time i, β is a learned coefficient vector from the current version of the GAME model, L is a loss function, b is a learned coefficient vector from a version the GAME model trained using data from the interval associated with time i−1, and λ is a regularization weight. The overall goal is to minimize the sum (because this function is evaluated for each data point in the relevant training data), as determined by modifying the values of β.

Once the random effect portions of the GAME model are (or are not) retrained for the time interval, the random effect offsets can be updated for each data point.

The above-described method provides several technical advantages over either the full training strategy involving training a full model during each retrain and a subset training strategy where only new data is used in training a model. Specifically, in contrast to the full training strategy, the above-described method reduces training resources to 1/K, where K is the number of time intervals into which the data is divided. There are the same number of random effects captured as before, and the random effect threshold allows a developer to trade off between recency and stability. A small random effects threshold, for example, prioritizes recent data while a large threshold prioritizes stable data.

Additionally, in contrast to the subset training strategy, all random effects are captured without using any more resources.

In some example embodiments, the threshold may be dynamically set and/or personalized. For example, certain members, or groups of members, may be assigned one threshold whereas other members, or groups of members, may be assigned a different threshold.

FIG. 5 is a flow diagram illustrating a method 500 for training a generalized additive mixed effect model, in accordance with an example embodiment. At operation 502, training data obtained from data in a social networking service is divided into a plurality of intervals based on time as indicated in time stamps in the data. Each interval is associated with a different value of successively increasing for each interval. At operation 504, a first set of features is derived from the training data for a first of the plurality of intervals. At operation 506, the first set of features is fed into a GAME model. The GAME model has a fixed effect portion and one or more random effect portions.

Then a loop is begun for each subsequent time interval. At operation 506, the fixed effect portion is retrained using fixed effect coefficients from a version of the fixed effect portion trained using data from the interval associated with time i−1, while converging on training data contained in the interval associated with time i. Then a loop is begun for each of one or more random effects contained in the training data in the interval associated with time i. At operation 508, it is determined if a number of data points corresponding to the random effect in the training data in the interval associated with time i transgresses a first threshold. If not, then at operation 510, a version of a random effect portion from the GAME model trained using data from the interval associated with time i−1 is reused. If so, then at operation 512, the random effect portion is trained or retrained using training data from the interval associated with time i. As described earlier, this training or retraining may be performed by minimizing ΣL(x, β)+λ*∥β−b∥²).

At operation 514, it is determined if there are any more random effects in the training data in the interval associated with time i. If so, then the method 500 loops back to operation 508 for the next random effect in the training data in the interval associated with time i. If not, then at operation 516, it is determined if there are any additional intervals to examine. If not then the method 500 ends. If so, then at operation 518, it is determined if convergence has occurred. This may include comparing a difference between output from a current version of the GAME model and the immediately preceding version of the GAME model to see if there is a significant enough difference to continue to train (e.g., if the difference exceeds a second threshold). If so, then the method 500 loops back to operation 506 for the next time interval. If not, then the method 500 ends. It should be noted that in an example embodiment each of the random effect training/retraining/reusing operations are computed in parallel, not in sequence.

In an example embodiment, the trained GAME model is used to make predictions useful for graphical user interface (GUI) presentation of potential feed items. For example, the likelihood that a viewer of the GUI would be interested in one or more feed items is used to determine which feed items to display and how to display then in the GUI.

FIG. 6 is a screenshot of a user feed 600 that includes items in different categories, according to some example embodiments. In the example embodiment of FIG. 6, the user feed 600 includes different categories, such as job recommendations 602, user posts 606, and sponsored items 608, and other embodiments may include additional categories.

In one example embodiment, the user feed 600 provides the job recommendations 602 (e.g., job posts 603 and 604) that match the job interests of the user.

The user posts 606 include items 607 posted by users of the social networking service, such as connections of the user, to make comments on the social networking service or include articles or webpages of interest.

The sponsored items 608 are items 609 placed by sponsors of the social networking service, which pay a fee for posting those items on user feeds, and may include advertisements or links to webpages that the sponsors want to promote.

Although the categories are shown as separated within the user feed 600, the items from the different categories may be intermixed, and not just be presented as a block. Thus, the user feed 600 may include a large number of items from each of the categories, and the social networking service decides the order in which these items are presented to the user based on the desired utilities. This may be based in part on the predictions output by the GAME model for this user.

FIG. 7 is a block diagram 700 illustrating a software architecture 702, which can be installed on any one or more of the devices described above. FIG. 7 is merely a non-limiting example of a software architecture, and it will be appreciated that many other architectures can be implemented to facilitate the functionality described herein. In various embodiments, the software architecture 702 is implemented by hardware such as a machine 800 of FIG. 8 that includes processors 810, memory 830, and input/output (I/O) components 850. In this example architecture, the software architecture 702 can be conceptualized as a stack of layers where each layer may provide a particular functionality. For example, the software architecture 702 includes layers such as an operating system 704, libraries 706, frameworks 708, and applications 710. Operationally, the applications 710 invoke API calls 712 through the software stack and receive messages 714 in response to the API calls 712, consistent with some embodiments.

In various implementations, the operating system 704 manages hardware resources and provides common services. The operating system 704 includes, for example, a kernel 720, services 722, and drivers 724. The kernel 720 acts as an abstraction layer between the hardware and the other software layers, consistent with some embodiments. For example, the kernel 720 provides memory management, processor management (e.g., scheduling), component management, networking, and security settings, among other functionality. The services 722 can provide other common services for the other software layers. The drivers 724 are responsible for controlling or interfacing with the underlying hardware, according to some embodiments. For instance, the drivers 724 can include display drivers, camera drivers, BLUETOOTH® or BLUETOOTH® Low Energy drivers, flash memory drivers, serial communication drivers (e.g., Universal Serial Bus (USB) drivers), Wi-Fi® drivers, audio drivers, power management drivers, and so forth.

In some embodiments, the libraries 706 provide a low-level common infrastructure utilized by the applications 710. The libraries 706 can include system libraries 730 (e.g., C standard library) that can provide functions such as memory allocation functions, string manipulation functions, mathematic functions, and the like. In addition, the libraries 706 can include API libraries 732 such as media libraries (e.g., libraries to support presentation and manipulation of various media formats such as Moving Picture Experts Group-4 (MPEG4), Advanced Video Coding (H.264 or AVC), Moving Picture Experts Group Layer-3 (MP3), Advanced Audio Coding (AAC), Adaptive Multi-Rate (AMR) audio codec, Joint Photographic Experts Group (JPEG or JPG), or Portable Network Graphics (PNG)), graphics libraries (e.g., an OpenGL framework used to render in two dimensions (2D) and three dimensions (3D) in a graphic context on a display), database libraries (e.g., SQLite to provide various relational database functions), web libraries (e.g., Web pit to provide web browsing functionality), and the like. The libraries 706 can also include a wide variety of other libraries 734 to provide many other APIs to the applications 710.

The frameworks 708 provide a high-level common infrastructure that can be utilized by the applications 710, according to some embodiments. For example, the frameworks 708 provide various GUI functions, high-level resource management, high-level location services, and so forth. The frameworks 708 can provide a broad spectrum of other APIs that can be utilized by the applications 710, some of which may be specific to a particular operating system 704 or platform.

In an example embodiment, the applications 710 include a home application 750, a contacts application 752, a browser application 754, a book reader application 756, a location application 758, a media application 760, a messaging application 762, a game application 764, and a broad assortment of other applications, such as a third-party application 766. According to some embodiments, the applications 710 are programs that execute functions defined in the programs. Various programming languages can be employed to create one or more of the applications 710, structured in a variety of manners, such as object-oriented programming languages (e.g., Objective-C, Java, or C++) or procedural programming languages (e.g., C or assembly language). In a specific example, the third-party application 766 (e.g., an application developed using the ANDROID™ or IOS™ software development kit (SDK) by an entity other than the vendor of the particular platform) may be mobile software running on a mobile operating system such as IOS™, ANDROID™, WINDOWS® Phone, or another mobile operating system. In this example, the third-party application 766 can invoke the API calls 712 provided by the operating system 704 to facilitate functionality described herein.

FIG. 8 illustrates a diagrammatic representation of a machine 800 in the form of a computer system within which a set of instructions may be executed for causing the machine to perform any one or more of the methodologies discussed herein, according to an example embodiment. Specifically, FIG. 8 shows a diagrammatic representation of the machine 800 in the example form of a computer system, within which instructions 816 (e.g., software, a program, an application 710, an apples, an app, or other executable code) for causing the machine 800 to perform any one or more of the methodologies discussed herein may be executed. For example, the instructions 816 may cause the machine 800 to execute the method 500 of FIG. 9. Additionally, or alternatively, the instructions 816 may implement FIGS. 1-5, and so forth. The instructions 816 transform the general, non-programmed machine 800 into a particular machine 800 programmed to carry out the described and illustrated functions in the manner described. In alternative embodiments, the machine 800 operates as a standalone device or may be coupled (e.g., networked) to other machines. In a networked deployment, the machine 800 may operate in the capacity of a server machine or a client machine in a server-client network environment, or as a peer machine in a peer-to-peer (or distributed) network environment. The machine 800 may comprise, but not be limited to, a server computer, a client computer, a PC, a tablet computer, a laptop computer, a netbook, a set-top box (STB), a portable digital assistant (PDA), an entertainment media system, a cellular telephone, a smartphone, a mobile device, a wearable device (e.g., a smart watch), a smart, home device (e.g., a smart appliance), other smart devices, a web appliance, a network router, a network switch, a network bridge, or any machine capable of executing the instructions 816, sequentially or otherwise, that specify actions to be taken by the machine 800. Further, while only a single machine 800 is illustrated, the term “machine” shall also be taken to include a collection of machines 800 that individually or jointly execute the instructions 816 to perform any one or more of the methodologies discussed herein.

The machine 800 may include processors 810, memory 830, and I/O components 850, which may be configured to communicate with each other such as via a bus 802. In an example embodiment, the processors 810 (e.g., a central processing unit (CPU), a reduced instruction set computing (RISC) processor, a complex instruction set computing (CISC) processor, a graphics processing unit (CPU), a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a radio-frequency integrated circuit (RFIC), another processor, or any suitable combination thereof) may include, for example, a processor 812 and a processor 814 that may execute the instructions 816. The term “processor” is intended to include multi-core processors that may comprise two or more independent processors (sometimes referred to as “cores”) that may execute instructions 816 contemporaneously. Although FIG. 8 shows multiple processors 810, the machine 800 may include a single processor with a single core, a single processor with multiple cores (e.g., a multi-core processor), multiple processors with a single core, multiple processors with multiple cores, or any combination thereof.

The memory 830 may include a main memory 832, a static memory 834, and a storage unit 836, all accessible to the processors 810 such as via the bus 802. The main memory 832, the static memory 834, and the storage unit 836 store the instructions 816 embodying any one or more of the methodologies or functions described herein. The instructions 816 may also reside, completely or partially, within the main memory 832, within the static memory 834, within the storage unit 836, within at least one of the processors 810 (e.g., within the processor's cache memory), or any suitable combination thereof, during execution thereof by the machine 800.

The I/O components 850 may include a wide variety of components to receive input, provide output, produce output, transmit information, exchange information, capture measurements, and so on. The specific I/O components 850 that are included in a particular machine 800 will depend on the type of machine 800. For example, portable machines such as mobile phones will likely include a touch input device or other such input mechanisms, while a headless server machine will likely not include such a touch input device. It will be appreciated that the I/O components 850 may include many other components that are not shown in FIG. 8. The I/O components 850 are grouped according to functionality merely for simplifying the following discussion, and the grouping is in no way limiting. In various example embodiments, the I/O components 850 may include output components 852 and input components 854. The output components 852 may include visual components (e.g., a display such as a plasma display panel (PDP), a light-emitting diode (LED) display, a liquid crystal display (LCD), a projector, or a cathode ray tube (CRT)), acoustic components (e.g., speakers), haptic components (e.g., a vibratory motor, resistance mechanisms), other signal generators, and so forth. The input components 854 may include alphanumeric input components (e.g., a keyboard, a touch screen configured to receive alphanumeric input, a photo-optical keyboard, or other alphanumeric input components), point-based input components (e.g., a mouse, a touchpad, a trackball, a joystick, a motion sensor, or another pointing instrument), tactile input components (e.g., a physical button, a touch screen that provides location and/or force of touches or touch gestures, or other tactile input components), audio input components (e.g., a microphone), and the like.

In further example embodiments, the I/O components 850 may include biometric components 856, motion components 858, environmental components 860, or position components 862, among a wide array of other components. For example, the biometric components 856 may include components to detect expressions (e.g., hand expressions, facial expressions, vocal expressions, body gestures, or eye tracking), measure biosignals (e.g., blood pressure, heart rate, body temperature, perspiration, or brain waves), identify a person (e.g., voice identification, retinal identification, facial identification, fingerprint identification, or electroencephalogram-based identification), and the like. The motion components 858 may include acceleration sensor components (e.g., accelerometer), gravitation sensor components, rotation sensor components (e.g., gyroscope), and so forth. The environmental components 860 may include, for example, illumination sensor components (e.g., photometer), temperature sensor components (e.g., one or more thermometers that detect ambient temperature), humidity sensor components, pressure sensor components (e.g., barometer), acoustic sensor components (e.g., one or more microphones that detect background noise), proximity sensor components (e.g., infrared sensors that detect nearby objects), gas sensors (e.g., gas detection sensors to detect concentrations of hazardous gases for safety or to measure pollutants in the atmosphere), or other components that may provide indications, measurements, or signals corresponding to a surrounding physical environment. The position components 862 may include location sensor components (e.g., a Global Positioning System (GPS) receiver component), altitude sensor components (e.g., altimeters or barometers that detect air pressure from which altitude may be derived), orientation sensor components (e.g., magnetometers), and the like.

Communication may be implemented using a wide variety of technologies. The I/O components 850 may include communication components 864 operable to couple the machine 800 to a network 880 or devices 870 via a coupling 882 and a coupling 872, respectively. For example, the communication components 864 may include a network interface component or another suitable device to interface with the network 880. In further examples, the communication components 864 may include wired communication components, wireless communication components, cellular communication components, near field communication (NFC) components, Bluetooth® components (e.g., Bluetooth® Low Energy), Wi-Fi® components, and other communication components to provide communication via other modalities. The devices 870 may be another machine or any of a wide variety of peripheral devices a peripheral device coupled via a USB).

Moreover, the communication components 864 may detect identifiers or include components operable to detect identifiers. For example, the communication components 864 may include radio frequency identification (RFID) tag reader components, NFC smart tag detection components, optical reader components (e.g., an optical sensor to detect one-dimensional bar codes such as Universal Product Code (UPC) bar code, multi-dimensional bar codes such as Quick Response (QR) code, Aztec code, Data Matrix, Dataglyph, MaxiCode, PDF417, Ultra Code, UCC RSS-2D bar code, and other optical codes), or acoustic detection components (e.g., microphones to identify tagged audio signals). In addition, a variety of information may be derived via the communication components 864, such as location via Internet Protocol (IP) geolocation, location via Wi-Fi® signal triangulation, location via detecting an NFC beacon signal that may indicate a particular location, and so forth.

Executable Instructions and Machine Storage Medium

The various memories (i.e., 830, 832, 834, and/or memory of the processor(s) 810) and/or the storage unit 836 may store one or more sets of instructions 816 and data structures (e.g., software) embodying or utilized by any one or more of the methodologies or functions described herein. These instructions (e.g., the instructions 816), when executed by the processor(s) 810, cause various operations to implement the disclosed embodiments.

As used herein, the terms “machine-storage medium,” “device-storage medium,” and “computer-storage medium” mean the same thing and may be used interchangeably. The terms refer to a single or multiple storage devices and/or media (e.g., a centralized or distributed database, and/or associated caches and servers) that store executable instructions 816 and/or data. The terms shall accordingly be taken to include, but not be limited to, solid-state memories, and optical and magnetic media, including memory internal or external to the processors 810. Specific examples of machine-storage media, computer-storage media, and/or device-storage media include non-volatile memory, including by way of example semiconductor memory devices, e.g., erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), field-programmable gate array (FPGA), and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM and DVD-ROM disks. The terms “machine-storage media,” “computer-storage media,” and “device-storage media” specifically exclude carrier waves, modulated data signals, and other such media, at least some of which are covered under the term “signal medium” discussed below.

Transmission Medium

In various example embodiments, one or more portions of the network 880 may be an ad hoc network, an intranet, an extranet, a VPN, a LAN, a WLAN, a WAN, a WWAN, a MAN, the Internet, a portion of the Internet, a portion of the PSTN, a plain old telephone service (POTS) network, a cellular telephone network, a wireless network, a Wi-Fi® network, another type of network, or a combination of two or more such networks. For example, the network 880 or a portion of the network 880 may include a wireless or cellular network, and the coupling 882 may be a Code Division Multiple Access (CDMA) connection, a Global System for Mobile communications (GSM) connection, or another type of cellular or wireless coupling. In this example, the coupling 882 may implement any of a variety of types of data transfer technology, such as Single Carrier Radio Transmission Technology (1×RTT), Evolution-Data Optimized (EVDO) technology, General Packet Radio Service (GPRS) technology, Enhanced Data rates for GSM Evolution (EDGE) technology, third Generation Partnership Project (3GPP) including 3G, fourth generation wireless (4G) networks, Universal Mobile Telecommunications System (UMTS), High-Speed Packet Access (HSPA), Worldwide Interoperability for Microwave Access (WiMAX), Long-Term Evolution (LTE) standard, others defined by various standard-setting organizations, other long-range protocols, or other data-transfer technology.

The instructions 816 may be transmitted or received over the network 880 using a transmission medium via a network interface device (e.g., a network interface component included in the communication components 864) and utilizing any one of a number of well-known transfer protocols (e.g., HTTP). Similarly, the instructions 816 may be transmitted or received using a transmission medium via the coupling 872 (e.g., a peer-to-peer coupling) to the devices 870. The terms “transmission medium” and “signal medium” mean the same thing and may be used interchangeably in this disclosure. The terms “transmission medium” and “signal medium” shall be taken to include any intangible medium that is capable of storing, encoding, or carrying the instructions 816 for execution by the machine 800, and include digital or analog communications signals or other intangible media to facilitate communication of such software. Hence, the terms “transmission medium” and “signal medium” shall be taken to include any form of modulated data signal, carrier wave, and so forth. The term “modulated data signal” means a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal.

Computer-Readable Medium

The terms “machine-readable medium,” “computer-readable medium,” and “device-readable medium” mean the same thing and may be used interchangeably in this disclosure. The terms are defined to include both machine-storage media and transmission media. Thus, the terms include both storage devices/media and carrier waves/modulated data signals. 

What is claimed is:
 1. A system comprising: a computer-readable medium having instructions stored thereon, when executed by a processor, cause the system to: divide training data obtained from data in a social networking service into a plurality of intervals based on time as indicated in time stamps in the data, each interval associated with a different value of i successively increasing for each interval; derive a first set of features from the training data for a first of the plurality of intervals; feed the first set of features into a generalized additive mixed effect (GAME) model, the GAME model producing a trained fixed effect portion and one or more trained random effects portions; for each subsequent time interval: retrain the fixed effect portion using fixed effect coefficients from a version of the fixed effect portion trained using data from the interval associated with time i−1 while converging on training data contained in the interval associated with time i; for each of one or more random effects contained in the training data in the interval associated with time i: reuse a version of a random effect portion from the GAME model trained using data from the interval associated with time i−1 if a number of data points corresponding to the random effect in the training data in the interval associated with time i does not transgress a first threshold.
 2. The system of claim 1, wherein the instructions further cause the system to: for each subsequent time interval: for each of one or more random effects contained in the training data in the interval associated with time i: train or retrain the random effect portion using training data from the interval associated with time i if the number of data points corresponding to the random effect in the training data in the interval associated with time i transgresses a first threshold.
 3. The system of claim 2, wherein the training or retraining includes minimizing ΣL(x, β)+λ*∥β−b∥² where x is a feature vector associated with one or more features extracted from the training data in the interval associated with time i, β is a learned coefficient vector from the a current version of the GAME model, L is a loss function, λ is a regularization weight, where b is the coefficient of the existing model.
 4. The system of claim 1, wherein the retraining is repeated until convergence, wherein convergence occurs when a subsequent version of the GAME model differs from an immediately preceding version of the GAME model by less than a second threshold.
 5. The system of claim 1, wherein the retraining further comprises updating fixed effect offsets of the fixed effect portion.
 6. The system of claim 2, wherein the training or retraining further comprises updating random effect offsets of the random effect portion.
 7. The system of claim 1, wherein the first threshold is dynamically set based on attributes of a first user to which a prediction to be output by the GAME model is associated.
 8. A computerized method comprising: dividing training data obtained from data in a social networking service into a plurality of intervals based on time as indicated in time stamps in the data, each interval associated with a different value of i successively increasing for each interval; deriving a first set of features from the training data for a first of the plurality of intervals; feeding the first set of features into a generalized additive mixed effect (GAME) model, the GAME model producing a trained fixed effect portion and one or more trained random effects portions; for each subsequent time interval: retraining the fixed effect portion using fixed effect coefficients from a version of the fixed effect portion trained using data from the interval associated with time i−1 while converging on training data contained in the interval associated with time i; for each of one or more random effects contained in the training data in the interval associated with time i: reusing a version of a random effect portion from the GAME model trained using data from the interval associated with time i−1 if a number of data points corresponding to the random effect in the training data in the interval associated with time i does not transgress a first threshold.
 9. The method of claim 8, further comprising: for each of one or more random effects contained in the training data in the interval associated with time i: training or retraining the random effect portion using training data from the interval associated with time i if the number of data points corresponding to the random effect in the training data in the interval associated with time i transgresses a first threshold.
 10. The method of claim 9, wherein the training or retraining includes minimizing ΣL(x, β)+λ*∥β−b∥² where x is a feature vector associated with one or more features extracted from the training data in the interval associated with time i, β is a learned coefficient vector from the a current version of the GAME model, L is a loss function, λ is a regularization weight, where b is the coefficient of the existing model.
 11. The method of claim 8, wherein the retraining is repeated until convergence, wherein convergence occurs when a subsequent version of the GAME model differs from an immediately preceding version of the GAME model by less than a second threshold.
 12. The method of claim 8, wherein the retraining further comprises updating fixed effect offsets of the fixed effect portion.
 13. The method of claim 9, wherein the training or retraining further comprises updating random effect offsets of the random effect portion.
 14. The method of claim 8, wherein the first threshold is dynamically set based on attributes of a first user to which a prediction to be output by the GAME model is associated with.
 15. A non-transitory machine-readable storage medium comprising instructions which, when implemented by one or more machines, cause the one or more machines to perform operations comprising: dividing training data obtained from data in a social networking service into a plurality of intervals based on time as indicated in time stamps in the data, each interval associated with a different value of i successively increasing for each interval; deriving a first set of features from the training data for a first of the plurality of intervals; feeding the first set of features into a generalized additive mixed effect (GAME) model, the GAME model producing a trained fixed effect portion and one or more trained random effects portions; for each subsequent time interval: retraining the fixed effect portion using fixed effect coefficients from a version of the fixed effect portion trained using data from the interval associated with time i−1 while converging on training data contained in the interval associated with time i; for each of one or more random effects contained in the training data in the interval associated with time i: reusing a version of a random effect portion from the GAME model trained using data from the interval associated with time i−1 if a number of data points corresponding to the random effect in the training data in the interval associated with time i does not transgress a first threshold.
 16. The non-transitory machine-readable storage medium of claim 15, further comprising: for each of one or more random effects contained in the training data in the interval associated with time i: training or retraining the random effect portion using training data from the interval associated with time i if the number of data points corresponding to the random effect in the training data in the interval associated with time i transgresses a first threshold.
 17. The non-transitory machine-readable storage medium of claim 16, wherein the training or retraining includes minimizing ΣL(x, β)+λ*∥β−b∥² where x is a feature vector associated with one or more features extracted from the training data in the interval associated with time i, β is a learned coefficient vector from the a current version of the GAME model, L is a loss function, λ is a regularization weight, where b is the coefficient of the existing model.
 18. The non-transitory machine-readable storage medium of claim 15, wherein the retraining is repeated until convergence, wherein convergence occurs when a subsequent version of the GAME model differs from an immediately preceding version of the GAME model by less than a second threshold.
 19. The non-transitory machine-readable storage medium of claim 15, wherein the retraining further comprises updating fixed effect offsets of the fixed effect portion.
 20. The non-transitory machine-readable storage medium of claim 16, wherein the training or retraining further comprises updating random effect offsets of the random effect portion. 